High speed multi-phase machine has drawn widely attention towards the development of electrification due to its high power density and fault tolerant capability. A 50 kW high speed nine-phase permanent magnet synchronous machine has been designed for more electric aircraft, of which the fundamental frequency is up to 2 kHz. Analysis in terms of stability, parameter sensitivity, system stiffness, transient and steady-state responses are carried out to compare the conventional proportional-integral (PI) and the complex vector current controllers. Simulation results show that the combination of complex vector current controller with virtual resistance and the improved anti-windup scheme is the best choice in all test aspects. What is more, by using the double sampling technique, the current THD is maintained less than 10% at the desired operation points when the switching frequency to fundamental frequency ratio ($R$) is above 10, and the system stability is maintained when the $R$ is only 5.